1. Field of the Invention
The present invention relates to a method and an apparatus for controlling tilt mirrors, which have been used in optical cross connects, optical add-drop multiplexers, optical routers, etc., in a WDM (Wavelength-Division Multiplexing) system which realizes high-speed, large-capacity data transmission.
2. Description of the Related Art
FIG. 13 is a perspective view in schematic form depicting a previously known optical tilt mirror that is actuated by electrostatic force. This electrostatic force-actuated tilt mirror has a tilt mirror 102 that can rotate about a torsion bar 101 and electrodes (underneath electrodes), 103 and 104, placed under the tilt mirror 102. By changing a voltage applied to the electrodes, 103 and 104, an electrostatic attraction given to the tilt mirror 102 is changed, thereby varying an angle at which the tilt mirror 102 is tilted. Note that such an electrostatic force-actuated tilt mirror is a micro-instrument implemented by MEMS (Micro Electro Mechanical Systems) technology.
Such electrostatic force-actuated tilt mirrors are arranged in array form to realize an optical switch. The number of the tilt mirrors is equal to the number of optical fibers coming in and going out. An optical path between arbitrary input and output optical fibers can be switched by changing the tilt angle of the tilt mirror 102.
When controlling such electrostatic force-actuated tilt mirrors, non-linearity of electrostatic capacity often becomes a problem. Electrostatic attraction is proportional to a value that is obtained by partially differentiating electrostatic energy with respect to a rotation angle, and its torque is given by:                                                         ∂                                                                                  ∂              θ                                ⁢                      (                                          1                2                            ⁢                              CV                2                                      )                          =                              1            2                    ⁢                                    ∂              C                                      ∂              θ                                ⁢                      V            2                                              (        1        )            
Although the non-linearity of electrostatic capacity can be suppressed by improving the construction of the electrodes or by limiting an action range (angle range) of the tilt mirror 102, a significant non-linearity due to the voltage squared term is difficult to control. Therefore, feedback control is utilized, or a square root calculating device in which an operational amplifier is combined with a diode is applied to the voltage, so as to speedup controlling of the tilt mirrors.
FIG. 14 illustrates an example square root calculation device, which is described in the following patent document 1. This square root calculation device is applicable to a control apparatus that performs feedback-control of an electrostatic actuator that exhibits non-linearity (see FIGS. 1 and 2 of the following patent document 1). The device has: a logarithmic calculation circuit 100 including a diode D1, a resistor R1, and an operational amplifier 100a; a ½ times circuit 110 including an operational amplifier 110a; an exponential circuit 120 including a diode D2, a resistor R2, and an operation amplifier 120a. Using an exponential-function-like current-voltage characteristic of the diodes, D1 and D2, the following calculation is performed: y=exp(0.5×1n(x))=√{square root over (x)}
The following patent document 2 discloses a feedback control technique for controlling the position of a sensor unit (movable unit) of an electrostatic acceleration sensor into position zero by electrostatic attraction, so that the non-linearity of such feedback control is avoided or reduced. Specifically speaking, on the basis of a differential signal which depends on a difference between the above movable unit and each of the electrodes sandwiching the movable unit therebetween, an electrostatic attraction of the electrodes is feedback-controlled by a microprocessor, which digitally filters (reducing noises and limiting band frequencies) and amplifies the differential signal, and which obtains the square root of the signal.
Other technologies related to tilt mirrors are disclosed in the following patent document 4 and 5. Moreover, a technology related to a spatial optical modulator is disclosed in the following patent document 3.
[Patent Document 1]
Japanese Patent Application Laid-open NO. HEI 2-241380 (from page 2, upper-right column, line 19 through page 3, upper-right column, line 4, and FIG. 5)
[Patent Document 2]
U.S. Pat. No. 5,277,053 (column 4, lines 10 through 45, and FIG. 1)
[Patent Document 3]
Japanese Patent Application Laid-open NO. HEI 9-101467
[Patent Document 4]
Japanese Patent Application Laid-open NO. HEI 10-142529
[Patent Document 5]
Japanese Patent Application Laid-open NO. HEI 9-159937
The above-described conventional technique has the following problems. First of all, the aforementioned documents 1 and 2 each employ a feedback control technique. In a case where MEMS tilt mirrors (hereinafter simply called MEMS mirrors) are to be controlled, their minuteness makes it difficult to incorporate any mirror angle detecting units therein. In particular, since a number of MEMS mirrors are required to form an optical mirror switch, such angle detecting units prepared, one for each of the MEMS mirrors, will affect practicality and cost performance of the system. In addition, even if such feedback control is successfully applied, thus allowing the tilt mirrors to settle down into their ideal angles sooner than they do by natural attenuation, a significant divergence, if any, from an ideal voltage characteristic delays the settlement.
Further, when a square root calculating device according to the above document 1 is applied, the current-voltage characteristic of a diode is given by the following formula (2), and strictly speaking, this is not an exponential function.                     I        =                  I          ⁢                                          ⁢          a          ⁢                      {                                          exp                ⁡                                  (                                                            q                      ⁢                                                                                          ⁢                      V                                                              k                      ⁢                                                                                          ⁢                      T                                                        )                                            -              1                        }                                              (        2        )            
Since a significant deviation appears in the vicinity of a voltage of 0 volt, some kind of correction, such as offset adjustment, is required. In addition, since the current-voltage characteristic of a diode is susceptible to temperature, and since variations among individual components need to be considered, the adjustment is required to be performed separately on each of the control objects.
Further, even if square root calculation is applied, it is still impossible to compensate for effects of the non-linearity [angular dependency of a value that is obtained by partially differentiating (angular differentiation) an electrostatic capacity C with respect to a mirror rotation angle θ] of electrostatic capacity against mirror rotation angles. Thus, a residual resonance frequency cannot be sufficiently suppressed.
Here, note that none of the technologies disclosed in the above patent document 3 through document 5 relates to controlling of a tilt mirror, and their features lie in the construction of a mirror itself or the construction of a spatial modulator. It is thus impossible to solve the foregoing problems using these technologies.